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On the data-driven COS method

Author

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  • Leitao, Álvaro
  • Oosterlee, Cornelis W.
  • Ortiz-Gracia, Luis
  • Bohte, Sander M.

Abstract

In this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based financial option valuation method which assumes the availability of asset data samples: a characteristic function of the underlying asset probability density function is not required. As such, the presented technique represents a generalization of the well-known COS method [1]. The convergence of the proposed method is O(1/n), in line with Monte Carlo methods for pricing financial derivatives. The ddCOS method is then particularly interesting for density recovery and also for the efficient computation of the option’s sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods.

Suggested Citation

  • Leitao, Álvaro & Oosterlee, Cornelis W. & Ortiz-Gracia, Luis & Bohte, Sander M., 2018. "On the data-driven COS method," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 68-84.
    • Handle: RePEc:eee:apmaco:v:317:y:2018:i:c:p:68-84
    DOI: 10.1016/j.amc.2017.09.002
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    References listed on IDEAS

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    8. Leitao, Álvaro & Grzelak, Lech A. & Oosterlee, Cornelis W., 2017. "On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 461-479.
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    Cited by:

    1. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "A data-driven framework for consistent financial valuation and risk measurement," European Journal of Operational Research, Elsevier, vol. 289(1), pages 381-398.
    2. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    3. Junike, Gero & Pankrashkin, Konstantin, 2022. "Precise option pricing by the COS method—How to choose the truncation range," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    4. Tobias Behrens & Gero Junike & Wim Schoutens, 2023. "Failure of Fourier pricing techniques to approximate the Greeks," Papers 2306.08421, arXiv.org, revised Nov 2024.
    5. Wenguang Yu & Yaodi Yong & Guofeng Guan & Yujuan Huang & Wen Su & Chaoran Cui, 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    6. Gero Junike, 2023. "On the number of terms in the COS method for European option pricing," Papers 2303.16012, arXiv.org, revised Mar 2024.
    7. Yanchun Zhao & Mengzhu Zhang & Qian Ni & Xuhui Wang, 2023. "Adaptive Nonparametric Density Estimation with B-Spline Bases," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    8. Yang, Yang & Su, Wen & Zhang, Zhimin, 2019. "Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 147-155.
    9. Gero Junike & Konstantin Pankrashkin, 2021. "Precise option pricing by the COS method--How to choose the truncation range," Papers 2109.01030, arXiv.org, revised Jan 2022.

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